circles | Systry - Free Printable

- Observations for r = a cos θ
- a is the radius.
- If a is positive, it's symmetric to the polar axis.
- If a is negative, it's symmetric to the polar axis reflected through the pole.

- Observations for r = a sin θ
- a is the radius.
- If a is positive, it's symmetric to the line θ = π/2.
- If a is negative, it's symmetric to the line θ = π/2 reflected through the pole.

- Observations for r = a cos nθ
- a is the length of each petal.
- If n is even, there are 2n petals.
- If n is odd, there are n petals.
- The first petal is symmetric with respect to the polar axis.
- Rotate petals by 360°/(2n) or 180°/n.

- Observations for r = a sin nθ
- a is the length of each petal.
- If n is even, there are 2n petals.
- If n is odd, there are n petals.
- The first petal is symmetric with respect to the line θ = π/(2n).
- Rotate petals by 360°/(2n) or 180°/n.

- r = -5 sin θ is a circle.
- 5 is the radius.
- Because the 5 is negative, the circle is reflected through the pole (origin).

- r = 2 cos 3θ is a rose curve.
- 2 is the length of each petal.
- Because n = 3, there are 3 petals.